Testing identity of high-dimensional covariance matrix

ABSTRACT

Two new statistics are proposed for testing the identity of high-dimensional covariance matrix. Applying the large dimensional random matrix theory, we study the asymptotic distributions of our proposed statistics under the situation that the dimension p and the sample size n tend to infinity proportionally. The proposed tests can accommodate the situation that the data dimension is much larger than the sample size, and the situation that the population distribution is non-Gaussian. The numerical studies demonstrate that the proposed tests have good performance on the empirical powers for a wide range of dimensions and sample sizes.

KEYWORDS:

• Identity hypothesis
• high-dimensional covariance matrix
• asymptotic distributions
• large dimensional random matrix theory

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Hao Wang   http://orcid.org/0000-0002-5539-0689

Additional information

Funding

This work was supported by Liaoning Planning Office of Philosophy and Social Science [No. 501100008339].